Angular momentum Definition and 1000 Threads

Homework Statement In a demonstration, a bicycle wheel with moment of inertia = .37 kg*m^2 is spun up to 14 rad/s, rotating about a vertical axis. A student hold the wheel while sitting on a rotatable stool. The student and the stool are initially stationary and have a moment of inertia equal...

I am considering the occurence of an incident circularly polarised EM wave on a ground state hydrogen atom. The result is that the final state of the atomic electron transition will be at m= ±1 depending on the orientation of polarisation (LCP or RCP). I understand that this is due to the...

Is it possible to derive ideas of angular momentum form linear momentum. Can linear momentum and calculus be used to derive ideas of angular momentum.

Homework Statement (see attachment) Homework Equations The Attempt at a Solution I think the angular momentum can be conserved about any point on the rod because torque is zero about any point on the rod. But that's not the correct answer. :confused: Any help is appreciated...

Suppose a rod is rotating about its center of mass, for simplicity consider it to be its geometric center(uniform density). At an instant a rigid ball is introduced near the rod so that it collides with the rod and the stick comes to rest(rotationally and translationally). Then can the ball be...

Here is an animation from Wikipedia : http://en.wikipedia.org/wiki/File:Torque_animation.gif The angular momentum is given by the Cross product of r and p We can see that the direction would be perpendicular to the direction of rotation of the particle (as shown in the animation) I don't...

Homework Statement For each of the following potential energy functions in three dimensions, what quantities are conserved (energy, momentum, angular momentum)?Homework Equations U = k/2(x^2 + y^2) U = α/r U = β(z(hat) dotted with r)^2 U = α/r + β(z(hat) dotted with r)^2 Where z(hat) is the...

I have 2 questions about the situations below http://img594.imageshack.us/img594/1/sadgsfdg.png Let vcp be the initial tangential velocity required for the upper body for that, when the low body is released, the upper body describes a circular trajectory I - In situation A, if we leave...

Homework Statement The Hamiltonian for two particles with angular momentum j_1 and j_2 is given by: \hat{H} = \epsilon [ \hat{\bf{j}}_1 \times \hat{\bf{j}}_2 ]^2, where \epsilon is a constant. Show that the Hamiltonian is a Hermitian scalar and find the energy spectrum.Homework Equations...

Hey, I'm not exactly sure how much this question wants, however the two in question are parts a) and b) below. So part a) asks to write the expression for the total angular momentum J, I though this was just: \hat{J}=\hat{J}^{(1)}+\hat{J}^{(2)} but when we come to showing it...

Consider a quantum system with angular momentum 1, in a state represented by the vector \Psi=\frac{1}{\sqrt{26}}[1, 4, -3] Find the expectation values <L_{z}> and <L_{x}> I'm reviewing my quantum mechanics; I had a pretty horrible course on it during undergrad. I feel like this should be...

While working on shooting mechanisms for the 2013 FIRST Robotics Competition, our mentoring scientist noted that the direction of the angular momentum vector pointed down for our prototype shooter. So now we're debating whether the vector points up or down matters for the flight of the frisbee...

Hey, My question is on determining an 'uncertainty' quantity using total angular momentum operators in the x,y and z directions where we know the commutation relations between the x,y and z directions of the total angular momentum operators. I'm not really sure where to go with this at...

Homework Statement A 1.7 kg , 20cm--diameter turntable rotates at 140rpm on frictionless bearings. Two 480g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. What is the turntable's angular velocity, in rpm , just after this event...

Hey, Also a bit confused on this one, the question is displayed below The possible total spin values are 1,0,-1 and I know that \mid l-s\mid\leq j\leq l+s\: ,\: -j\leq m_{z}\leq j Where the latter inequality is in integer steps, so I'm not really sure if it is as simple as...

Hey, My question is on the probability of attaining a particular eigenvalue for the total angular momentum operator squared for a particular state ψ, the question is shown in the image below: I believe the eigenvalue of the total angular momentum operator squared is given by j(j+1)...

Homework Statement A mass m is laying on a frictionless table and is connected to a mass M with a nonelastic string going through the center of the table. At t=0 the m mass is at a r0 distance from the center of the table, and is moving at a v0 velocity in the tangent direction. Find the...

Homework Statement Alright apologies I could not attach an image due to my inexperience of this but its simple to imagine. Imagine a stick which can rotate about the centre of its axis, perpendicular to its length. I.e the ends can rotate freely in a clockwise, or anti clockwise manner...

[Li,Lj]=εijkLk how can I prove this expression classically?

Homework Statement How to prove that for any representation of the spin, the state e^{-i{\pi}J_x/\hbar}|j,m\rangle is proportional to |j,-m\rangle The exponential term is the rotation operator where J_x is the x-component of the total angular momentum operator, and |j,m\rangle is an...

This is not a homework problem. I am trying to set up the following problem. I am doing something wrong. Help. I have attached the problem and figure but here is the text. Figure 10-52 shows a thin, uniform bar of Length L and mass M and a small blob of putty of mass m. The system is...

hi pf, i got following questions in my mind while reading about the spin angular momentum of an electron. 1. From rotational dynamics we know that to have angular momentum a body must necessarily rotation or motion? so does an electron rotates as it has spin angular momentum or does it...

I want to find [M_i, M_j] Poisson brackets. $$[M_i, M_j]=\sum_l (\frac{\partial M_i}{\partial q_l}\frac{\partial M_j}{\partial p_l}-\frac{\partial M_i}{\partial p_l}\frac{\partial M_j}{\partial q_l})$$ I know that: $$M_i=\epsilon _{ijk} q_j p_k$$ $$M_j=\epsilon _{jnm} q_n p_m$$ and so...

Homework Statement I have attached the question as jpg to this post. Typing these were too time consuming and I uploaded the relevant sections as image files, thanks for your understanding. Homework Equations mu_0*epsilon_0*Poynting Vector = Momentum density Position vector X...

What is the angular momentum of a rod rotating about one end (mass M and angular velocity ш),about its center of mass?

I had read in a book that the primary reason for the use of tail rotor in a helicopter is to counteract the rotation of the main body generated as a response to the rotation of the main rotor blades to keep angular momentum of the rotor-body system zero. Is it true that the rotation of main...

Homework Statement Two particles A and B having equal masses m are rotating around a fixed point O with constant angular speed ω .A is connected to point O with a string of length L/2 whereas B is connected to point A with string of length L/2 .Find the angular momentum of B with respect to...

Hi, I am by now very used to the concept of conservation of momentum and energy, however i had never solved a problem using the conservation of angular momentum. Well, in the case where angular momentum is conserved, we do not have a torque net. But, how this conservation law helps us to...

let us denote the joint eigenstate of \hat{L^{2}}and \hat{L_{z}} by ll,m> and we know that if we are in spherical coordinates, \hat{L^{2}} and \hat{L_{z}} depend on θ and ∅, so we denote the joint eigenstate by: <θ∅l l,m>.. why?

Homework Statement Dear all, This is my first post and I need some help. The exercise I am trying to solve is this one: A star has a radius of 6 × 10^8 m and a period of rotation of 30 days. Eventually it becomes a neutron star with a radius of 10^4 m and a period of 0.1 s. If the...

Homework Statement Problem with diagram here Homework Equations I=(1/3)MR2 (I believe the formula given in the problem is incorrect since it is pivoting on one end rather than the center of mass) KE=(1/2)Iω2+(1/2)Mv2 L=Iω=MvR The Attempt at a Solution a. True, the velocity is still going in...

Homework Statement Suppose the system is rotating clockwise when the metal disk is dropped on it. The direction of the frictional force is... zero on the disk and the system counter-clockwise on the disk, clockwise on the system clockwise on the disk, zero on the system...

Hello, Does the Conservation of Angular Momentum have any relation to the rapid rotation of Pulsars? I've reasoned that the Angular Momentum of the "parent" star would be concentrated on the smaller pulsar and would produce a greater frequency of rotation. Thanks,

Imagine i have a particle in the xy plane rotating in a circle around the z-axis at a constant angular velocity. The angular momentum is r cross p which would give me a constant value at all times, there is no change and it's conserved. However if I was to move the rotating particle higher up...

Suppose there was a mass, m1, traveling rightwards at v0. There is a second mass, m2, above the line of motion of m1, and which has a rigid, massless bar of length L attached to its center of mass. This bar extends downwards so that the terminal intersects with the path of m1. When m1 reaches...

Hello, I am currently reading about angular momentum. A sentence in my textbook sort of confused me: "when the translational velocity of the particle is along a line that passes through the axis, the particle has zero angular momentum with respect to the axis." I was wondering if someone...

Homework Statement A man, mass M, stands on a massless rod which is free to rotate about its center in the horizontal plane. The man has a gun (massless) with one bullet, mass m. He shoots the bullet with velocity Vb, horizontally. Find the angular velocity of the man as a function of the angle...

Homework Statement What are the orbital angular momentum possible values for an electron in a hydrogen atom with a principal quantum number n = 3? Homework Equations L = \sqrt{l(l+1)}\hbar The Attempt at a Solution Possible values for l are 0, 1, 2. So, substituting these in...

okay, i realize that the angular momentum of a moving point mass could be looked at about any point, and that angular momentum is conserved as long as no torque is acted on that point mass. but, something i don't understand is how, then, the angular velocity could increase if the moment of...

Number 11) This is what I did: Ʃτ = F2r2 + F1r1 = 0 (195)(7) + F1(0.7) = 0 F1(0.7) = -(195)(7) F1 = -1365/0.7 F1 = -1950 N F1 = 1950 N Is that answer right? Number 12) This is what I did: Since this is a massless rod and the location of the axis is through the end, I = ML2 Linitial =...

Homework Statement A 1.47kg particle moves in the xy plane with a velocity of v = (4.59i - 3.28j)m/s. Determine the magnitude of the particle's angular momentum when its position vector is r = (1.35i + 2.57j)m. Homework Equations p = mv L = r x p (the x is supposed to be a cross...

Homework Statement consider the possible angular momentum states |s,m>, of a system of two spin-1/2 particles construct all possible states with total spin zero (S=0) Homework Equations The Attempt at a Solution if total S of system is zero, m must also equal zero. So the...

Why exactly is it necessary for angular momentum to be lost by a mass if it is to accrete around a black hole? the mass is decreasing its radius, so it speeds up: thus angular mometum is conserved. But everywhere it is saying that 99.99% of the angular momentum must be shed for accretion to...

Homework Statement A 0.478-kg ball is thrown at a 22.3-cm tall, 0.383-kg object and hits with a perfectly horizontal velocity of 12.8 m/s. Suppose the ball strikes at the very top of the object. After collision the ball has a horizontal velocity of 4.6 m/s in the same direction. The object...

Friction causes a torque that opposes angular momentum. It gets reduced. how can we derive a relation connecting these. friction starts with maximum and becomes zero. angular velocity and its corresponding momentum decreases maximum in the beginning and increases towards the end. the radial...

Homework Statement A heavy stick of length L = 3.3 m and mass M = 20 kg hangs from a low-friction axle. A bullet of mass m = 0.014 kg traveling at v = 117 m/s strikes near the bottom of the stick and quickly buries itself in the stick. Just after the impact, what is the angular speed ω of...

I know the approach is to use conservation of angular momentum. I also know that I am entirely free to pick which point I would like to calculate my L about. (Although calculating L about the CM will make it much easier, but I'd like to try otherwise) So, if I were to calculate my L(after...

Calculate angular momentum? I almost got the right answer but it's wrong! Help! This is what I did for part a... 1. What is given Particle mp = 0.450 kg ω = 2.00 rad/s r = 1 m Stick ms = 0.125 kg ω = 2.00 rad/s r = 0.5 m 2. Angular momentum is conserved (Linitial = Lfinal)...

Determining the work done on the puck using conservation of angular momentum?? Help! This is what I did... 1) Given mpuck = 0.300 kg rinitial = 0.4 m vinitial = 0.6 m/s mpuck = 0.300 kg rfinal = 0.15 m vfinal = ____ m/s ƩW = KEfinal - KEinitial 2) KEinitial = (1/2)mv2...

Homework Statement A rod of length l swivels around an axis, denoted O in the drawing, located on the floor. The initial position is β=45°. A ball B is left to fall at the same time the rod is left to rotate. Who will arrive, first, to the floor: the ball or the edge A of the rod...